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Normality testing after outlier removal

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  • Berenguer-Rico, Vanessa
  • Nielsen, Bent

Abstract

The cumulant based normality test after outlier removal is analyzed. It is shown that the standard least squares normalizations can be misleading in this context. The sample cumulants should be standardized according to the truncation imposed at the removal stage and the estimation method being used. New standardizations that lead to chi-squared inference are derived.

Suggested Citation

  • Berenguer-Rico, Vanessa & Nielsen, Bent, 2026. "Normality testing after outlier removal," Econometrics and Statistics, Elsevier, vol. 38(C), pages 74-96.
    • Handle: RePEc:eee:ecosta:v:38:y:2026:i:c:p:74-96
    DOI: 10.1016/j.ecosta.2023.06.001
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    References listed on IDEAS

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    1. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "The analysis of marked and weighted empirical processes of estimated residuals," Economics Papers 2019-W03, Economics Group, Nuffield College, University of Oxford.
    2. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    3. Vanessa Berenguer-Rico & Ines Wilms, 2021. "Heteroscedasticity testing after outlier removal," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 51-85, January.
    4. Thorsten Thadewald & Herbert Buning, 2007. "Jarque-Bera Test and its Competitors for Testing Normality - A Power Comparison," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 87-105.
    5. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    6. Søren Johansen & Bent Nielsen, 2016. "Rejoinder: Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 374-381, June.
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